Welcome!
What most people have done with a similar fan/light set up where the light is controlled by a pull cord on the fan is to replace the switch that controls the fan itself with a fan switch. There’s one from GE and one from Leviton, so if you are using other GE switches The one from GE will match nicely.
Then they put a in wall microcontroller up near the fan that only controls the lights. So essentially you are just replacing the pull cord with this other device.
Finally, they will put a battery operated switch or a handheld remote elsewhere in the room that can tell the microcontroller to turn the lights on or off.
So that gives you separate control of the fan and the light.
@dalec did exactly this and describes the equipment he used:
Some other community members have just put a smart light bulb in the fan and then again controlled that with a battery operated device. That can work well depending on the style of the fan. There aren’t any chandelier size smart bulbs that are compatible with SmartThings. But some fans use the regular A19 bulbs, and then you can use any of the smart bulbs that work with SmartThings.
Obviously using an In wallmicro requires some wiring but since it’s just for the lights, not the fan motor, it’s pretty simple for an electrician to do.
There aren’t any micros that I can think of that handle A variable speed ceiling fan well – – the fan switches are a better fit for that piece of the project. The GE model is the 12730.
https://www.amazon.com/GE-Control-Z-Wave-12730-Amazon/dp/B00PYMGVVQ